From Parents to Peers: Trajectories in Sources of Academic Influence Grades 4 to 8

Abstract

Prior research and anecdotal evidence from educators suggest that classroom peers play a meaningful role in how students learn. However, the literature has failed to consider the dynamic and context-dependent nature of classroom peer influence. Developmental psychology theories suggest that peer influence will increase and family influence will decrease as children enter adolescence. This study uses rich administrative data from North Carolina in 2006 to 2012, matching students to all peers in each of their courses in third through eighth grades. The analysis identifies trends in the magnitude of classroom peer effects across grade levels, with special attention to controlling for confounding factors such as simultaneous influence, student–classroom sorting, nonlinearity, and school-type effects. Consistent with psychological theories about adolescence, our findings indicate that the effect of average peer quality multiplies by a factor of nearly 3 for reading and 5 for math between fourth grade and seventh grade; contemporaneously, family socioeconomic status effects on academic performance nearly vanish by the end of middle school. We uncover additional evidence that ability grouping, while often harmful in an elementary school setting, becomes increasingly beneficial in later grades—particularly for math subjects.

Keywords

adolescence child development econometric analysis economics of education educational policy peer interaction/friendship regression analyses secondary data analysis social processes/development

All children, except one, grow up.

—J. M. Barrie, The Adventures of Peter Pan

Introduction

From the rapidly growing literature on academic peer effects, we know that school peers can have a significant and lasting influence on a student’s learning and motivation (Sacerdote, 2014). High-achieving students can inspire and motivate their classmates, whereas low-achieving students may disrupt others’ learning. In fact, some studies conclude that differences in peer composition can be at least as important as those in teacher quality for explaining variation in student academic achievement (Graham, 2008). If this is the case, policies and practices that shape how students sort into schools and classrooms may be as critical for improving educational outcomes as teacher training, curriculum setting, or other traditional instructional inputs.

Most prior research from K–12 school environments has estimated the magnitude of peer effects as an average across students in multiple grades or multiple school settings (such as elementary school or middle school). Reviews of the literature have also attempted to compare peer effect estimates directly across studies that make use of samples with varied age groups and contexts (Epple & Romano, 2011). Such comparisons rely on an assumption that peer influence operates as a single construct independent of student age and school setting. However, this practice conflicts with a body of literature in psychology indicating that peer influence is not consistent across individual development and grows dramatically during adolescence in other domains such as antisocial and risky behavior (Steinberg & Monahan, 2007). Furthermore, the onset of middle school and its changes in classroom structure and older peer exposure have been found to increase disciplinary infraction rates and reduce reading test scores (Cook, Macoun, Muschkin, & Vigdor, 2008).

The primary objective of the current study is to trace the developmental trajectory of academic peer influence. We hypothesize that because adolescents are increasingly likely to turn to their peers for role-modeling and guidance in the social realm, they may therefore increasingly tend to mimic academic efforts and behaviors of students to whom they are frequently exposed. This study uses a rich longitudinal administrative data set of students in North Carolina matched to their classroom peers from Grades 3 to 8. In doing so, we employ strategies to minimize three major empirical challenges for estimating endogenous social effects: simultaneity, selection bias, and nonlinearity (Manski, 1993). Furthermore, our study examines whether factors typically confounded with age—such as the classroom structure and organization of middle and elementary schools, and teacher characteristics—account for classroom peer effects. A secondary objective is to examine the direct and indirect impacts of school setting type, defined by the configuration of peers of varying ages within the same building (e.g., Grades K–6, 6–8, K–8), on student test performance.

We find strong grade-level trends in the magnitude of classroom peer effects, increasing year by year through seventh grade before plateauing. Our measurement of peer effects includes both direct social interaction effects and potential responses from instructors to different classroom compositions. The grade-level effects clearly originate from student age and cannot be accounted for by school-type or grade configuration. The value of classroom homogeneity in terms of academic ability also rises across student development. But as strong academic peer influence emerges in adolescence, something else must give. We find that coming from a low-income household, as measured imperfectly by having ever been eligible for free or reduced lunch (FRL), has declining influence on educational achievement as students age and enter adolescence.

This study contributes empirically to the peer effects literature by identifying differences in academic peer influence by grade and school type, and theoretically to the general field of education production functions. Our results indicate that the technology of education production shifts considerably across the course of student development, suggesting that future research should more fully incorporate and highlight these dynamics.

Summary of Academic Peer Effects Literature

Research on the identification of peer effects in academic settings has proliferated in the past decade. Manski (1993) detailed challenges and problematic assumptions in estimating social interaction effects, but a number of researchers have nonetheless taken up this task. More comprehensive reviews of the literature are provided by Sacerdote (2014); Sacerdote (2010); and Epple and Romano (2011). Studies have uncovered significant peer effects across disparate settings, for example, classrooms, hospital rooms, prison cells, military companies, and college dorms (Epple & Romano, 2011; Kulik, Mahler, & Moore, 1996; Ouss, 2011). For those studies focusing on K–12 school peer effects, wide disparities exist in the point estimates from linear-in-means models. For example, Vigdor and Nechyba (2007) report negligible peer effects once they restrict their sample to schools with quasirandom assignment and include teacher and school fixed effects. Betts and Zau (2004), however, find that a 1.0-point move in average peer score increases student reading and math score gains by 1.4 and 1.9 points, respectively.

The current study tests one important potential source of heterogeneity among peer effects estimates: the age of students. Burke and Sass (2013) estimate peer effects separately for elementary, middle, and high school students, but do not attempt a more fine-grained estimate of the age trajectory in academic peer influence. Our study is also not the first to make use of North Carolina student-level data. Vigdor and Nechyba (2007) estimate academic peer influence for elementary school students and find negligible effects. Also focusing on elementary school grades, Frueworth (2013) analyzes peer achievement spillovers within race-based reference groups and considers potential distributional impacts of school desegregation. And finally, a recent article uses North Carolina data to examine whether increases in Latin American immigrant or limited English students have any impact on the learning of native students (Diette & Oyelere, 2017). We are fortunate to possess course membership data with a longer grade span than most of these prior studies, including previously unavailable access to student–teacher matched data in middle school grades.

Recent peer effects studies have also made significant advances in identification strategies and attention to nonlinearities. This body of research has striven to exploit plausibly exogenous variation in peer environments—such as randomized classroom assignment, cross-cohort differences, or student mobility—to attain unbiased estimates of peer effects. It has also compared traditional linear-in-means models with more complex functional forms and identified interaction effects of a student’s own ability with his or her peers’ ability. Although the current study uses a simple identification strategy, we build off of this earlier empirical research and pay careful attention to the critical issues of endogeneity and nonlinearity.

Developmental Theory of Peer Influence

In 1970, two parallel studies theorized that conformity to peers increases from middle childhood to adolescence due to rising social pressures from peer groups (Bronfenbrenner, 1970; Devereux, 1970). The rise in peer conformity is accompanied by a commensurate decline in parental influence and is thought to be an adaptive, evolved mechanism to prepare a child for entering adulthood and participating in the commons (Dietz, Ostrom, & Stern, 2003). A number of experimental and survey studies in psychology have confirmed this hypothesized trend (e.g., Berndt, 1979; Costanzo & Shaw, 1966; Gardner & Steinberg, 2005; Steinberg & Monahan, 2007). One main objective of this line of research has been to examine “deviant peer contagion” and to assess the role of peer influence in adolescents’ propensity for risky behaviors (Gonzales & Dodge, 2010).

This article contributes to this literature by testing this trend in the domain of academic achievement and by translating the research from child and adolescent psychology to an economic framework. In this vein, we introduce a simple modification to the education production function model in the following subsection, accounting for how students may increasingly develop peer orientation (or move away from family orientation) as they progress through schooling. This specification of the education production function, in which the technology itself can update dynamically, is less restrictive than standard models of student achievement, and has direct implications for policy.

Dynamic Education Production Technology

Todd and Wolpin (2003) carefully delineate the assumptions of various empirical specifications for estimating impacts of educational inputs on cognitive achievement. To justify the common value-added approach, they list two necessary conditions among others: (a) The technology function is non-age-varying, at least over the ages used in implementing a value-added model; and (b) for gain score models, the effect of each input must be independent of the age at which it was applied. This study considers the validity of these claims, focusing on the less traditional educational input domains of peer groups and family socioeconomic background.

Academic achievement $A_{t}$ at any given time t can be thought of as a function of school factors such as instructional quality and grade-level configuration $(S_{t})$ , a student’s peer environment $(P_{t})$ , and outside-of-school factors such as family background $(F_{t})$ . This is described generically in the equation below:

A_{t} = f_{t} (P_{t}, S_{t}, F_{t}, ε_{t}) .

According to developmental theory introduced in the previous section, individuals tend to shift in adolescence from relying heavily on parents to orienting themselves toward conformity with their peer groups. Berndt (1979) found that conformity to peers for prosocial and antisocial behaviors peaked sometime between sixth and ninth grade. Our central hypothesis therefore is that the relative academic influence of peers increases across years of schooling $t$ until some peak is reached at time $t^{*}$ , with $P_{t}$ in this equation representing a scalar measure that indexes peer quality:

\frac{\partial A_{t}}{\partial P_{t}} > \frac{\partial A_{t - 1}}{\partial P_{t - 1}} for all t \leq t^{*} .

A relative decrease in the salience of family factors, $\partial A_{t} / \partial F_{t}$ , would likely accompany the observed shift toward peer orientation. Although our information on family background is not as detailed as the data on exposure to school peers, we are still able to consider the question of whether the salience of family and economic background characteristics (as measured by a scalar index of family resources for academic achievement $F_{t}$ ) diminishes across years of schooling:

\frac{\partial^{2} A_{t}}{\partial F_{t}^{2}} < 0 for all t < t^{*} .

Another testable feature of this model of education is whether peer influence intensifies as a consequence of the transition from elementary school to middle school apart from any direct age- or grade-level changes. Eccles et al. (1993) apply the theory of stage-environment fit to understanding the transition to middle school from elementary school. They note that changes in classroom organization, composition, and practices upon entering middle school tend to exacerbate social comparison and competitiveness among students—reason to believe that structural features of middle school intensify academic peer effects. The formal version of this hypothesis is as follows:

\frac{\partial A_{m t}}{\partial P_{m t}} > \frac{\partial A_{e t}}{\partial P_{e t}} for all t .

In this equation, $m$ and $e$ represent the two main school types: middle school and elementary school. As we observe both fifth graders in elementary school and fifth graders in middle school in our data (and sixth graders in both types of schools), we can identify these school-type effects separately from grade effects.

Other scholars (e.g., Epple & Romano, 1998; Nechyba, 2000) have simulated the welfare implications of public and private school choice mechanisms such as voucher programs. They based these theoretical simulations on the assumption that schools with higher ability students have positive peer effects on students who choose to attend. Our study, as it pursues its central hypotheses H1, H2, and H3, may illuminate whether such school choice mechanisms would be more or less effective for different grade levels and school types based on the grade-level-gradient of peer composition effects.

Data and Method

Data Set

This analysis takes advantage of rich administrative data from the North Carolina Education Research Data Center (NCERDC). Course membership data match students to each of their enrolled courses and teachers and track them longitudinally from the 2005–2006 to 2011–2012 school years. For students in Grades 3 through 8, we have detailed information on their school, teachers, coursework, and End of Grade (EOG) standardized test scores in mathematics and reading comprehension. These annual scores serve as our outcome of interest and also as a measure of classroom peers’ ability levels. We normalize the scores by grade and year to have a mean of 0 and standard deviation of 1. Because the regressions require lagged test scores to control for student ability, our analytical sample excludes students in the third grade (for whom no scores are available in second grade) or in the first available school year, 2005–2006.

Each student has two relevant peer groups per year: his or her primary math classroom and his or her primary English or language arts (ELA) classroom. Math and ELA classes with unusually low or unusually high class sizes (fewer than seven or more than 33 students) are excluded. These class size outliers represent less than 5% of all math and ELA classrooms. Peer ability variables such as mean peer score are calculated from prior year EOG scores of the set of all students in the current classroom of Student i, excluding Student i him or herself. The final sample includes, approximately, 1.7 million student-year observations enrolled in nearly 2,000 schools and matched to over 20,000 teachers.

Identification of Peer Effects

The “Introduction” section described some of the primary challenges for identifying endogenous social interaction effects in school settings. We are concerned with three main empirical issues that could bias results: (a) the simultaneous equations problem that peer effects are bidirectional between a student and his or her peers, (b) the selection problem that students do not sort into classrooms randomly, and (c) the functional form problem that linear-in-means models may insufficiently identify effects from the full distribution of peer achievement. We are also concerned with another confounding variable specific to this study—school type. If there appears, as predicted, a rise in the magnitude of peer influence between Grades 4 and 8, how much of that growth derives from age-related changes versus structural changes between elementary schools and middle schools? To address this concern, we perform several school-type and grade-configuration robustness checks, described in more detail in the “Results” section.

To ameliorate problems of simultaneity, we construct peer ability variables from the prior year test scores of a student’s current year classroom peers. In this way, there is no opportunity for a student’s own academic effort to affect his or her classmates’ prior performance. To account for classroom selection mechanisms, we control for student ability through the prior year test score and teacher observable and unobservable factors through teacher fixed effects. Course tracking would only bias our peer effect estimates if there are unobserved components of student ability correlated with classroom placement in Year t but unrelated to student performance in the same subject in Year t − 1.

Equations 1 and 2 represent our two primary linear-in-means models for estimating grade-level trends in academic peer influence. In Model 1, Student i’s achievement in Classroom c, School s, Grade g, and Year t is a function of subject-specific peer prior achievement and a number of other variables.

\begin{array}{l} A_{i c s g t} = β_{0} + β_{1} A_{i t - 1} + β_{2} \bar{A_{c t - 1}} + \\ β_{3} (\bar{A_{c t - 1}} \times I [g = 5]) + \dots + \\ β_{7} (\bar{A_{c t - 1}} \times I [g = 8]) + \\ β_{8} X_{i} + θ_{s} + δ_{g} + α_{t} + ε_{i c s g t} . \end{array}

In this equation, $A_{i t - 1}$ represents prior year student achievement, and $X_{i}$ is a vector of student characteristics including gender, race, gifted status, exceptionality status, FRL eligibility, parental education, limited English proficiency, and prior grade retention and suspension. Model 1 includes $\bar{A_{c t - 1}}$ , the average prior achievement of current classroom peers, as well as a series of grade-level interaction terms with this mean peer score, $(\bar{A_{c t - 1}} \times I [g = 5]) + \dots + (\bar{A_{c t - 1}} \times I [g = 8])$ . The estimated parameters, $β_{3}$ through $β_{7}$ , therefore test whether the magnitude of peer effects changes significantly by grade level. Finally, this model includes school fixed effects ( $θ_{s}$ ), grade fixed effects ( $δ_{g}$ ), and year fixed effects ( $α_{t}$ ). In all models, we include a cubic function of classroom size although the model is robust to other class size parametric specifications.

Model 2, shown below, is largely identical to Model 1, except for the inclusion of teacher fixed effects ( $γ_{j}$ ):

\begin{array}{l} A_{i c j g t} = β_{0} + β_{1} A_{i t - 1} + β_{2} \bar{A_{c t - 1}} + \\ β_{3} (\bar{A_{c t - 1}} \times I [g = 5]) + \dots + \\ β_{7} (\bar{A_{c t - 1}} \times I [g = 8]) + \\ β_{8} X_{i} + γ_{j} + δ_{g} + α_{t} + ε_{i c j g t} . \end{array}

Importantly, the use of teacher fixed effects allows us to exploit within-teacher differences in classroom composition, across time or within a single school year, to identify academic peer effects. This alleviates the concern that teacher quality is likely correlated with classroom composition. However, it is still probable that teachers respond differently to different classroom groups in terms of their pacing and instructional style. For this reason, teachers’ responses to changes in classroom composition still constitute one possible mechanism of the estimated peer effects. Because of correlated errors within schools and classrooms, we cluster standard errors by both teacher and school.¹

Other researchers, in similar attempts to minimize the selection problem of students to classrooms, have chosen to include student fixed effects in their models (Arcidiacono, Foster, Goodpaster, & Kinsler, 2012; Burke & Sass, 2013). This approach holds both advantages and disadvantages. Unlike the lagged test score method, student fixed effects would control for any unobservable student characteristics that are constant across time, instead of reliance upon a single proxy measure. However, this method introduces several drawbacks. First, there is a problem of reverse causality: If a student’s score in Time t has a direct influence on his or her classroom peer group in Time t + 1, as is the case in any school with ability tracking, demeaning dependent and independent variables by student creates a systematic downward bias (Rivkin, 2007). In fact, when we perform a simulation exercise with artificially constructed data, and allow a student’s score in Year t to somewhat inform the assignment of classroom peers in Year t + 1, the model with a lag score leads to a downward bias of peer effects of less than 0.01 SDs and the model with student fixed effects leads to a downward bias of greater than 0.21 SDs. For this reason, we exclude student fixed effects and instead control for student prior ability using his or her prior math and reading test scores.

A final variation on this model tests for grade-level trends in the impacts of the dispersion of classroom peer achievement. In Equation 3, we have added an independent variable of the standard deviation of prior achievement of a student’s classroom peers, $S D (A_{c t - 1})$ :

\begin{array}{l} A_{i c j g t} = β_{0} + β_{1} A_{i t - 1} + β_{2} \bar{A_{c t - 1}} + \\ β_{3} (\bar{A_{c t - 1}} \times I [g = 5]) + \dots + \\ β_{7} (\bar{A_{c t - 1}} \times I [g = 8]) + \\ β_{8} S D (A_{c t - 1}) + \\ β_{9} (S D (A_{c t - 1}) \times I [g = 5]) + \dots + \\ β_{13} (S D (A_{c t - 1}) \times I [g = 8]) + \\ β_{14} X_{i} + γ_{j} + δ_{g} + α_{t} + ε_{i c j g t} . \end{array}

This model includes interaction terms of grade-level indicators with the standard deviation of peer achievement, (SD(A _ct–1 )× $I [g = 5]) + \dots + (S D (A_{c t - 1}) \times I [g = 8]) .$ It offers one simple method for examining effects of the distribution of peer achievement. Prior peer effect studies, not designed specifically for considering the developmental trajectories of academic peer influence, have estimated more intricate models of peer effects that uncover nonlinearities in interaction effects between the student’s and peers’ ability levels (Burke & Sass, 2013; Hoxby & Weingarth, 2005). We aim not to replicate these efforts, but rather to determine in the most straightforward manner possible whether effects of peer heterogeneity on student achievement change as students age.

Results

For students in North Carolina elementary and middle schools, classroom peers factor significantly into cumulative academic learning. Even once we account for student ability and characteristics, school fixed effects, and teacher fixed effects, classroom composition remains an important predictor of student achievement. In Table 1, we observe that a one standard deviation increase in mean peer prior achievement raises individual achievement by 0.081 SDs in reading and 0.087 SDs in math. This effect includes two potential mechanisms. First, a student’s effort is likely influenced directly by peers’ behavior, either through observation of peers’ effort or through reinforcement by peers of a student’s studying and performance. Second, as mentioned previously, teachers may differentially tailor their pacing and instructional style to the abilities of each group of students they encounter.

Table 1

Basic Impacts of Classroom Peer Achievement on Reading and Math Scores

	Reading (1)	Math (1)	Reading (2)	Math (2)
Lagged test score	0.6396** (0.001)	0.6590** (0.002)	0.6396** (0.001)	0.6617** (0.001)
Mean lagged peer score	0.0827** (0.002)	0.0855** (0.003)	0.0809** (0.002)	0.0869** (0.003)
SD of lagged peer scores	0.0082* (0.004)	−0.0246** (0.006)	0.0105** (0.003)	−0.0137** (0.005)
Fixed effects
School	X	X
Teacher			X	X
Grade	X	X	X	X
Year	X	X	X	X
Observations	1,665,374	1,706,037	1,665,374	1,706,037
R ²	.635	.669	.610	.656
Number of schools	1,981	1,984
Number of teachers			21,554	20,471

Note. Robust standard errors in parentheses, clustered by teacher and school; coefficients on student-level covariates omitted.

†

p < .1. *p < .05. **p < .01.

The coefficient estimates on the standard deviation of peer achievement differ across subjects. In ELA classrooms, higher variance in peer achievement has a modest positive impact on student performance (0.011 SDs). However, in math classrooms, higher variance in peer achievement instead suppresses individual performance (by 0.014 SDs). Therefore, it appears that students’ reading comprehension skills may in fact benefit from classroom peers with diverse levels of ability. However, in math, it is more advantageous for students to be matched with peers at a similar level of prior performance. We examine the degree to which these basic findings differ by grade level in the subsection below.

Estimates of Grade-Level Trends

To test the central question of this study about the emergence of “peer orientation,” we regress student achievement on mean peer achievement, interacted with grade-level indicators and a host of controls (see Equation 1). Results are generally consistent across Model 1 with school fixed effects and Model 2 with teacher fixed effects, so we discuss only the Model 2 results from columns 3 and 4 in Table 2. As Model 1 does not fully control for the nonrandom sorting of students to teachers, we expect Model 2 with teacher fixed effects to provide more conservative peer effect estimates. In math classrooms, the baseline peer effect in fourth grade is 0.023 SDs, but increases to 0.108 SDs by the seventh grade before leveling off. Baseline peer effects in ELA classrooms are 0.034 SDs and also increase to a peak in sixth grade of 0.098 SDs. All of these results are statistically significant. Figure 1 shows this marked rise across grades, and Table 2 formally demonstrates the trend statistically.²

Table 2

Effect of Mean Peer Achievement: Grade-Level Interactions

	Reading (1)	Math (1)	Reading (2)	Math (2)
Lagged test score	0.6396** (0.001)	0.6590** (0.002)	0.6392** (0.001)	0.6611** (0.001)
Mean lagged peer score	0.0565** (0.004)	0.0498** (0.006)	0.0340** (0.005)	0.0232** (0.006)
Interaction terms
Peer score × Grade 4	(omitted)	(omitted)	(omitted)	(omitted)
Peer score × Grade 5	0.0245** (0.005)	0.0135 (0.008)	0.0314** (0.006)	0.0171* (0.007)
Peer score × Grade 6	0.0486** (0.005)	0.0656** (0.008)	0.0638** (0.005)	0.0806** (0.007)
Peer score × Grade 7	0.0136** (0.005)	0.0441** (0.007)	0.0443** (0.005)	0.0845** (0.007)
Peer score × Grade 8	0.0260** (0.005)	0.0285** (0.007)	0.0474** (0.005)	0.0570** (0.007)
Fixed effects
School	X	X
Teacher			X	X
Grade	X	X	X	X
Year	X	X	X	X
Observations	1,871,313	1,918,939	1,871,310	1,918,936
R ²	.684	.718	.693	.744
Number of schools	1,981	1,984
Number of teachers			21,580	20,483

Note. Robust standard errors in parentheses, clustered by teacher and school; coefficients on student-level covariates omitted.

†

p < .1. *p < .05. **p < .01.

Figure 1.

Effects of mean prior peer achievement by grade level.

These results support our hypotheses. The salience of peers for educational learning increases as children enter adolescence and peaks around sixth grade for ELA classrooms and seventh grade for math classrooms. To contextualize the magnitude of these peer effects, a one standard deviation increase in peer test scores during the peak adolescence period has an impact equal to just under one half of the total learning a student gains on average between sixth and seventh grade. However, our findings do contradict an earlier study that found that middle school students actually exhibit lower classroom peer effects than elementary school students (Burke & Sass, 2013). We believe this difference could stem from their use of student fixed effects, which could introduce downward bias especially in later middle school grades when ability tracking is common.

The plateau of peer effects in sixth grade for reading and seventh grade for math, and the subsequent slight decline, may at first seem puzzling. However, there is some precedent. For example, Berndt (1979) performed experiments with children and adolescents in 3rd, 6th, 9th, and 12th grades in which the individual responded to hypothetical situations testing either conformity to peers or conformity to parents on antisocial and prosocial behaviors. He found that the age trends for conformity were curvilinear and that peer conformity peaked at ninth grade for antisocial behavior and sixth grade for prosocial behavior. Our study observes a corresponding critical moment of peer influence during middle school in the academic domain, followed by what appears to be a period of slight decline. We perform a series of Wald coefficient equality tests and confirm that each stand-alone grade-to-grade change is statistically significant, except for the difference in ELA peer effects between Grades 7 and 8 and the difference in math peer effects between Grades 6 and 7.³

In the earlier section describing a dynamic education production technology, we hypothesized that any increase in peer influence that occurs while children enter adolescence may occur alongside a proportional decline in the importance of parents and family background for academic performance. This is challenging, but not impossible, to formally test with the available student data. We have information on the FRL eligibility status of students, which can be used as an imperfect proxy for family socioeconomic disadvantage. To address the concern that uptake and/or reporting of FRL status differs greatly by grade level, we use a single measure of whether or not the student has ever been eligible for FRL. Therefore, any changes of the association of FRL eligibility with test score growth across grade levels should reflect true differences in the impact of our proxy measure of low family socioeconomic status, not differences in the measure’s definition or implementation.

We run regressions of Model 2 and include interaction terms of FRL status with grade-level indicators. The trends in Figure 2 indicate that the negative impacts of living in a low-income household (as measured by FRL eligibility) diminish across grades and dissipate entirely by seventh grade in this model, controlling for school-level factors. The results are suggestive and consistent with the theory that as children transition into adolescence, the school peer environment becomes more important than the family environment for predicting behavior and academic performance. For adolescent students in middle school grades, our findings show that there exists an opportunity to undo, with either classroom organization, school assignments, or school-level policies, some of the detrimental educational effects of coming from a low-income household.

Figure 2.

Marginal effects of free or reduced lunch eligibility by grade level.

Nonlinear Peer Effect Trend Estimates

The linear-in-means framework for estimating peer effects is appealing, but this specification does not reflect the totality of peer influence within a classroom (Hoxby & Weingarth, 2005), which also includes the influence of the diversity of peers. Therefore, this study also tests a separate mechanism of peer effects using the variance of prior peer achievement. We estimate regressions in the form of Model 3 (see Equation 3) to determine whether the second order moment of classmates’ achievement matters and, furthermore, whether this association changes across grade levels. As can be seen in Table 3 and Figure 3, the impact of dispersion in peer achievement does shift significantly as grade level increases.

Table 3

Effect of Variance of Peer Achievement: Grade-Level Interactions

	Reading (1)	Math (1)	Reading (2)	Math (2)
Lagged test score	0.6396** (0.001)	0.6591** (0.001)	0.6392** (0.001)	0.6611** (0.001)
SD of lagged peer score	0.0228** (0.008)	0.0182 (0.013)	0.0343** (0.009)	0.0082 (0.012)
Interaction terms
Peer score SD × Grade 4	(omitted)	(omitted)	(omitted)	(omitted)
Peer score SD × Grade 5	−0.0039 (0.012)	−0.0238 (0.019)	−0.0162 (0.012)	−0.0049 (0.015)
Peer score SD × Grade 6	−0.0222^† (0.012)	−0.0198 (0.021)	−0.0249* (0.012)	−0.0116 (0.016)
Peer score SD × Grade 7	−0.0192 (0.011)	−0.0688** (0.019)	−0.0271* (0.011)	−0.0285^† (0.015)
Peer score SD × Grade 8	−0.0099 (0.010)	−0.0850** (0.019)	−0.0252* (0.011)	−0.0244^† (0.015)
Fixed effects
School	X	X
Teacher			X	X
Grade	X	X	X	X
Year	X	X	X	X
Observations	1,665,374	1,706,037	1,665,374	1,706,037
R ²	.635	.669	.610	.656
Number of schools	1,981	1,984
Number of teachers			21,554	20,471

Note. Robust standard errors in parentheses, clustered by teacher and school; coefficients on student-level covariates omitted.

†

p < .1. *p < .05. **p < .01.

Figure 3.

Effects of prior peer achievement classroom variance by grade level.

In ELA fourth-grade reading classrooms, a one standard deviation increase in the standard deviation of peer prior performance significantly raises individual achievement in reading by 0.034 SDs. However, this positive effect declines in Grades 5, 6, and 7, becoming statistically indistinguishable from 0 by Grade 6. Model 1 estimates, with school fixed effects instead of teacher fixed effects, show the same general trend, although the fourth-grade coefficient is 0.02 rather than 0.03. In math classrooms, we uncover the same grade-level trend, but with lower overall effects of peer achievement variance. In fourth grade, the standard deviation of prior achievement of math classmates has no significant effect on individual math scores. This coefficient decreases through Grade 7 and then levels off. Seventh grade is the only time at which the standard deviation of prior peer math achievement has a statistically negative effect on student performance (−0.029 SDs).

Across both reading and math samples, heterogeneous-ability classrooms are relatively more effective in earlier grades, and homogeneous-ability classrooms are more effective in later grades. This pattern corresponds somewhat to the timing that many schools use for introducing ability tracking, which given our findings, seems an effective moment to introduce the practice. Although prior research does not provide any clear justification for why classroom homogeneity promotes learning, more so in later grade levels, we believe that advanced course content could require teachers to target their curriculum to a particular ability level, more so than more basic course content.

Our results suggest that, while ability tracking practices in math classrooms that begin around seventh grade may promote aggregate math performance, tracking in ELA classrooms is on average not beneficial (and sometimes quite harmful). Hoxby and Weingarth (2005) describe this phenomenon of positive classroom heterogeneity effects as the “Rainbow Model,” and suggest students could learn the answer to a question more deeply when they see it approached from a variety of angles. A few key studies confirm this finding for ELA classrooms. Fierro (2014), for example, found that students performed better in mixed ability ELA classrooms than in tracked classrooms, with positive and statistically significant improvements for low-ability students and positive but statistically insignificant improvements for high-ability students. Hanushek and Woessman (2006) found that countries with tracking in primary school classrooms had 1.053 SDs lower reading scores (p < .01) but 0.597 SDs higher science scores (p < .05). And Vigdor and Nechyba (2007) also find statistically significant, positive effects of classroom heterogeneity in North Carolina schools.

Role of School-Type and Grade Configurations

Up to this point, we have interpreted results from a child development perspective and ignored the possibility that school-level or grade configuration may account for grade-level trends of peer influence. The degree and type of exposure to classroom peers likely changes as students progress from elementary to middle school settings, and that could potentially account for some differences in the magnitude of peer effects across grades. We are able to test this alternate hypothesis directly using geographical variance of school grade structures across North Carolina. Cook et al. (2008) note that the differences in middle school grade configurations across North Carolina tend to exist because of idiosyncratic school changes that happened in response to swelling cohort sizes in the 1970s and after. For our analysis, we focus first only on fifth and sixth graders who attend different types of schools. For example, some fifth graders attend elementary school (K–5), others middle school (5–8), and still others attend schools with other types of grade configurations (K–8, etc.). If the grade-level rise in academic peer influence we observed earlier is driven by school structure rather than age differences, we would expect a stronger peer effect for fifth graders in middle schools than for fifth graders in elementary schools.

We test this hypothesis formally for fifth and sixth graders in Table 4 using school-type and mean peer score interaction terms. The results indicate conclusively that school type does not drive our results regarding the emergence of peer effects during adolescence. The mean peer effects for both fifth graders and sixth graders are constant across school types, with the sole exception that peer influence is slightly stronger in K–12 schools in fifth-grade reading. This analysis implies that the rise in salience of classroom peers has less to do with external school factors and more to do with internal changes in how students relate to and learn from their peers.

Table 4

School-Type Robustness Check

	Reading (Grade 5)	Math (Grade 5)	Reading (Grade 6)	Math (Grade 6)
Lagged test score	0.6628** (0.002)	0.7085** (0.002)	0.6253** (0.002)	0.6252** (0.002)
Mean lagged peer score	0.0439** (0.005)	0.0117* (0.006)	0.0957** (0.003)	0.1107** (0.003)
School-type interactions
(Grades K–5) × Peer score	(omitted)	(omitted)
(Grades 5–8) × Peer score	0.0412 (0.027)	0.0306 (0.020)
(Grades K–8) × Peer score	0.008 (0.023)	0.0346 (0.029)
(Grades K–12) × Peer score	0.0523* (0.023)	0.0651^† (0.040)
(Other types) × Peer score	0.0097 (0.020)	0.0200 (0.024)
(Grades 6–8) × Peer score			(omitted)	(omitted)
(Grades K–6) × Peer score			0.0193^† (0.010)	0.0272 (0.021)
(Grades K–8) × Peer score			0.0006 (0.011)	0.0001 (0.017)
(Grades K–12) × Peer score			−0.0065 (0.021)	0.0104 (0.020)
(Other types) × Peer score			0.0154 (0.013)	−0.0079 (0.026)
Fixed effects
Teacher	X	X	X	X
Grade	X	X	X	X
Year	X	X	X	X
Observations	269,430	284,439	372,811	377,020
R ²	.595	.656	.616	.658
Number of teachers	7,069	6,699	3,892	3,653

Note. Robust standard errors in parentheses, clustered by teacher and school; coefficients on student-level covariates and school-type indicators omitted.

†

p < .1. *p < .05. **p < .01.

Another approach for disentangling age trends in peer influence from structural school changes is to compare directly the age trends within each school type. Appendixs A1 and A2 in the online version of the journal present these results for mathematics and reading, and indicate that age-level trends in peer influence persist across a number school types with different grade configurations: K–5, K–6, K–8, 5–8, and K–12. Although individual peer effect coefficients do differ somewhat across school types, each type experiences a significant rise in the magnitude of peer influence as grade levels increase. The schools with less common grade configurations, such as K–6 or 5–8, have smaller sample sizes and therefore larger standard errors. So, for example, although reading peer effects in fourth grade at a K–6 school are statistically insignificant, the point estimate does not differ largely from that of a K–5 school (0.022–0.028). We also compare the trend lines from estimates of grade-specific peer effects with estimates of peer effects by age as a cubic function and find remarkably similar shapes (see Online Appendix Figure A5).

Robustness Tests

We perform several robustness tests to check for bias in our basic identification of peer effects. One concern is that even when using prior year peer quality measures, there is still opportunity for what Manski (1993) labels the “reflection problem,” that a student’s own achievement and that of his or her peers may interact reciprocally over time. To minimize sources of this bias, we reestimate peer effects with a simple sample restriction. In particular, we restrict the main sample to only students who transferred from a different school for the current school year. Although in this case the likelihood that students have long-term prior social interaction history with their peers diminishes, the principal results remain quite similar. The mean peer effect decreases from 0.165 to 0.140 SDs in reading and 0.328 to 0.262 SDs in math. This slight decrease suggests that peer effects may indeed to a small degree be reciprocal and cumulative over time. Full results appear in the Online Appendix Table A3.

This sample restriction still does not fully address the potential problem that school tracking introduces for unbiased estimation of classroom peer effects. If unobservable aspects of student ability directly affect the peer composition of a student’s classroom (which would likely be the case under many tracked classroom assignment practices), then our peer effect estimates would suffer from upward bias. To address this issue, we perform a robustness test inspired by methods used in Vigdor and Nechyba (2007). First we exclude any school-grade-year-subjects with fewer than two classrooms. Then for each school-grade-year-subject, we compute a Wilks’ lambda multiple-group multivariate comparison statistic to test whether all classrooms within that school-grade-year-subject have equivalent mean prior student math and reading test scores. If we can reject the hypothesis of equivalent means across classrooms in that group with 90% confidence, we label these classrooms “non-random assignment.” If we fail to reject the hypothesis of equivalent means across classrooms, we label these classrooms as “random assignment.” Online Appendix Tables A4 and A5 present results from the random student assignment sample of classrooms. Overall, it appears that our average peer effect estimates are 0.01 to 0.02 SDs too large due to student selection bias, but our estimates of the grade-level gradient in peer effects could be underestimated by 0.07 SDs.

Discussion

The evidence from this study supports the hypothesis that classroom peers play a growing role in the educational process across age. Our results indicate that all benefits, or consequences, from classroom composition heighten as students move from childhood to adolescence. These findings suggest the need for schools (and especially for schools containing sixth and seventh grades) to devote careful attention not only to selection of teachers to classrooms, but also to the assignment of groups of students to classrooms. We conclude that these grade-level shifts in peer influence cannot be attributed to transitions between different school types. Instead, they are likely a consequence of an individual’s tendency to shift during adolescent development from conforming to parents and authority, to conforming to his or her same-age peers.

This study also confirms prior evidence that academic peer effects are not limited to a linear-in-means framework. Although peer influence appears to operate differently math and ELA classrooms, we uncovered an important trend in the effects of the level of dispersion of peer academic achievement. In fourth grade, increases in the variance of classroom peer achievement improve student reading performance (and do not harm student math performance). Classrooms with diverse levels of student ability outperform those with more homogeneous groups of students in the earlier grades. However, as students progress across grade levels, this benefit eventually disappears. By seventh grade, increased variance of peer achievement no longer improves student reading scores and even harms math performance.

Research in the field of economics of education often makes tradeoffs about necessary simplifications of education production functions to estimate the salience of different school factors, for example, teacher quality, school resources, class size, or peer effects. However, this study and other strands of research indicate that the technology of education production is dynamic and interacts with both individual student attributes and the environmental or school context. Our findings demonstrate that the estimated return to one of these educational inputs—school peers—varies by a student’s developmental stage. In an interesting symmetry, our results also illustrate how the marginal impact of family socioeconomic status wanes across student development.

We believe that detailing this type of heterogeneity in peer effects or other educational inputs provides a valuable next step for translating econometric research to educational practices. We return to the interesting trend from Figure 2, which demonstrates how the absolute value of the coefficient on an FRL indicator diminishes as students progress through school, even though the measure is constructed to be identical across grades for a single student. This pattern reflects the common notion that individuals turn to parents as role models early in life, but their attitudes and behaviors shift during adolescence to mimic more closely those of their peers. In our data and the context of academic achievement, this means that although low socioeconomic status is still a great burden to students early on in their schooling, it may hold less import relatively than one’s school environment later on in middle school years.

From an educational perspective, we see clear evidence that whereas antipoverty and family support policies are well-suited for households with younger children, policies that affect the sorting of students into schools and across classrooms could have enormous educational impact for adolescent-age students.

Footnotes

Acknowledgements

We are grateful to the North Carolina Education Research Data Center for access to and assistance with data used in this project.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: Sorensen’s contribution was supported in part by a predoctoral fellowship provided by the National Institute of Child Health and Human Development (T32-HD07376-25) through the Center for Developmental Science, University of North Carolina at Chapel Hill.

Notes

Authors

Lucy C. Sorensen is an assistant professor in the Rockefeller College of Public Affairs and Policy at the University at Albany, State University of New York. Her research empirically examines questions at the intersection of education policy, human development, and social inequality. Email: lsorensen@albany.edu

Philip J. Cook is the ITT/Sanford Professor of Public Policy, professor of economics, and professor of sociology at Duke University. His research in education policy has focused on causal modeling of the determinants of educational achievement. Email: pcook@duke.edu

Kenneth A. Dodge is the William McDougall Professor of Public Policy Studies and professor of psychology and neuroscience at Duke University. His research investigates the development and prevention of violent behaviors and evaluates effects of child and family policies on those outcomes. Email: dodge@duke.edu

References

Arcidiacono

Foster

Goodpaster

Kinsler

(2012). Estimating spillovers using panel data, with an application to the classroom. Quantitative Economics, 3, 421–470.

Berndt

T. J.

(1979). Developmental changes in conformity to peers and parents. Developmental Psychology, 15, 608–616.

Betts

J. R.

Zau

(2004). Peer groups and academic achievement: Panel evidence from administrative data. Unpublished Manuscript, Public Policy Institute of California, USA.

Bronfenbrenner

(1970). Reaction to social pressure from adults versus peers among Soviet day school and boarding school pupils in the perspective of an American sample. Journal of Personality and Social Psychology, 15, 179–189.

Burke

M. A.

Sass

T. R.

(2013). Classroom peer effects and student achievement. Journal of Labor Economics, 31, 51–82.

Cameron

A. C.

Miller

D. L.

(2015). A practitioner’s guide to cluster-robust inference. Journal of Human Resources, 50, 317–372.

Cook

P. J.

Macoun

Muschkin

C. G.

Vigdor

(2008). The negative impacts of starting middle school in sixth grade. Journal of Policy Analysis and Management, 27, 104–121.

Costanzo

P. R.

Shaw

M. E.

(1966). Conformity as a function of age level. Child Development, 37, 967–975.

Devereux

E. C.

(1970). The role of peer group experience in moral development. In Hill

John P.

(Ed.), Minnesota symposium on child psychology (Vol. 4, pp. 94–140). Minneapolis: University of Minnesota Press.

10.

Diette

T. M.

Oyelere

R. W.

(2017). Gender and racial differences in peer effects of limited English students: A story of language or ethnicity? IZA Journal of Migration, 6(1), 2.

11.

Dietz

Ostrom

Stern

P. C.

(2003). The struggle to govern the commons. Science, 302, 1907–1912.

12.

Eccles

J. S.

Midgley

Wigfield

Buchanan

C. M.

Reuman

Flanagan

Mac Iver

(1993). Development during adolescence: The impact of stage-environment fit on young adolescents’ experiences in schools and in families. American Psychologist, 48, 90–101.

13.

Epple

Romano

R. E.

(1998). Competition between private and public schools, vouchers, and peer group effects. The American Economic Review, 88, 33–62.

14.

Epple

Romano

R. E.

(2011). Peer effects in education: A survey of the theory and evidence. In Benhabib

Basin

Jackson

M. O.

(Eds.), Handbook of social economics (Vol. 1B, pp. 1053–1163). San Diego, CA: Elsevier.

15.

Fierro

C. M.

(2014). Does how students are assigned to classrooms matter? An examination of relative achievement in tracked and untracked middle grades language arts classrooms. Available from ProQuest Dissertations and Theses database. (UMI No. 3707824)

16.

Frueworth

J. C.

(2013). Identifying peer achievement spillovers: Implications for desegregation and the achievement gap. Quantitative Economics, 4, 85–124.

17.

Gardner

Steinberg

(2005). Peer influence on risk taking, risk preferences, and risky decision making in adolescence and adulthood: An experimental study. Developmental Psychology, 41, 625–635.

18.

Gonzales

Dodge

K. A.

(2010). Family and peer influences on adolescent behavior and risk-taking. Unpublished Paper submitted to the National Research Council and Institute of Medicine’s Board on Children, Youth, and Families.

19.

Graham

B. S.

(2008). Identifying social interactions through conditional variance restrictions. Econometrica, 76, 643–660.

20.

Hanushek

E. A.

Woessman

(2006). Does educational tracking affect performance and inequality? Differences-in-differences evidence across countries. The Economic Journal, 116, C63–C76.

21.

Hoxby

C. M.

Weingarth

(2005). Taking race out of the equation: School reassignment and the structure of peer effects (Working Paper No. 7867). Cambridge, MA: Harvard University.

22.

Kulik

Mahler

Moore

(1996). Social comparison and affiliation under threat effects on recovery from major surgery. Journal of Personality and Social Psychology, 71, 967–979.

23.

Manski

C. F.

(1993). Identification of endogenous social effects: The reflection problem. Review of Economic Studies, 60, 531–542.

24.

McPherson

Smith-Lovin

Cook

J. M.

(2001). Birds of a feather: Homophily in social networks. Annual Review of Sociology, 27, 415–444.

25.

Nechyba

T. J.

(2000). Mobility, targeting, and private-school vouchers. The American Economic Review, 90, 130–146.

26.

Ouss

(2011, December). Prisons as a school of crime: Evidence from cell-level interaction (Working paper). Cambridge, MA: Harvard University.

27.

Rivkin

(2007). Value-added analysis and education policy (Brief 1). Washington, DC: National Center for Analysis of Longitudinal Data in Education Research (CALDER).

28.

Sacerdote

(2010). Peer effects in education: How might they work, how big are they and how much do we know thus far? In Hanushek

E. A.

Machin

S. J.

Woessmann

(Eds.), Handbook of the economics of education (Vol. 3, pp. 249–277). Amsterdam, The Netherlands: North Holland.

29.

Sacerdote

(2014). Experimental and quasi-experimental analysis of peer effects: Two steps forward? Annual Review of Economics, 6, 253–272.

30.

Steinberg

Monahan

K. C.

(2007). Age differences in resistance to peer influence. Developmental Psychology, 43, 1531–1543.

31.

Todd

P. E.

Wolpin

K. I.

(2003). On the specification and estimation of the production function for cognitive achievement. The Economic Journal, 113, F3–F33.

32.

Vigdor

J. L.

Nechyba

T. S.

(2007). Peer effects in North Carolina public schools. In Peterson

P. E.

Woessman

(Eds.), Schools and the equal opportunity problem (pp. 73–101). Cambridge, MA: MIT Press.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.14 MB